Fraction Simplifier

Enter a fraction and simplify it to its lowest terms.

Simplify Fractions

Fraction

Result

What is a Simplified Fraction?

A simplified fraction is one where the greatest common divisor (GCD) of the numerator and denominator is 1. In other words, it is a fraction that cannot be reduced further. Simplifying fractions makes calculations easier and more intuitive.

How to Simplify a Fraction?

To simplify a fraction, follow these steps:

Identify the type of fraction: proper fraction, improper fraction, or mixed fraction. If it's a mixed fraction, convert it to an improper fraction first.
Calculate the greatest common divisor (GCD) of the numerator and denominator.
Divide both the numerator and denominator by the GCD to get the simplified fraction.

Example 1: Simplify the fraction \(\frac{18}{24}\).

Solution:

1. Find the GCD:

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

GCD of 18 and 24 is 6

2. Divide the numerator and denominator by 6:

\( \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \)

Thus, the simplified form of \(\frac{18}{24}\) is \(\frac{3}{4}\).

Example 2: Simplify the mixed fraction \(2\frac{2}{4}\).

Solution:

1. Convert the mixed fraction to an improper fraction:

\( 2\frac{2}{4} = \frac{2 \times 4 + 2}{4} = \frac{10}{4} \)

2. Find the GCD of 4 and 10:

GCD(4, 10) = 2

3. Divide the numerator and denominator by 2:

\( \frac{10 \div 2}{4 \div 2} = \frac{5}{2} \)

So, the simplified form of \(2\frac{2}{4}\) is \(2\frac{1}{2}\).